Mixed confine fusion experiment, evidence of feasibility of confinement

Introduction

Nuclear fusion occurs with a huge amount of energy released. In order to use fusion energy as an energy supplier, thermonuclear fusion is used, which requires devices confining hot plasma. It seems that limitations exist in all kinds of fusion devices. For example, pressure produced on the coils is observed in almost all kinds of fusion devices using magnetic field as a driver, such as Tokamak, which was proposed by USSR scientist G.G.Dolgov-Saveliev.^1,2 A much higher standard of material for the wall exists in other devices using inertia as the driver in inertial confinement fusion (ICF), which uses the method of very rapidly heating and compressing small pellets of suitable fuel.³ Lasers are used as drivers in ICF. This method causes the first wall to be exposed to more X-ray and debris meaning the wall must be made using a higher standard of material.⁴ Other fusion device using both magnetic field and inertia as the drivers of confinement like Magneto-internal fusion (MIF), have been designed using magnetic field to confine a low density plasma and then lasers are used, compressing the hot plasma until fusion occurs.⁵ Laser is used as the main driver to achieve fusion. Magnetized laser fusion, a liner which is a tube magnetically imploded is contained and used to heat and compress to achieve the condition of fusion,⁶ suffer both of the limitations mentioned in tokamak and ICF.

Mixed confine fusion (MCF), is a promising method of confining plasma proposed in the 2022 3rd International Conference on Materials, Physics and Computers (MPC 2022), is mainly about confining fusion plasma with a high speed change of three perpendicular magnetic field, using both magnetic field and inertia as drivers, in which some limitations might be avoided. Different from MIF, MCF uses magnetic field in the final stage to achieve fusion. As a consequence of this method not only does no extra laser need to be used, but in addition, the magnets are all used periodically, which causes a lower average pressure per time of the magnets as an interval of rest is produced. This allows for a much lower standard of electric magnet is required. Different from other devices using both magnetic field and inertia as drivers, in MCF, these two drivers are used equally, while in MIF magnetized laser fusion laser is the main driver to achieve fusion and magnetic field is used for initial confinement.⁵ MCF is considered as having some advantages comparing with Tokamak. It is shown with a simulated model (used in a previous study by the author) that there is no force exist in the center of the model, leading to a suitable distribution of energy for plasma confinement.⁷ At the same time, the limitation of the MCF method is that the ability of confinement of plasma is much weaker when compared with Tokamak is shown as the overall energy difference between the edge of the model and the center, which is considered as the cause of force of confinement, is much smaller than Tokamak in similar conditions.⁷

However, in my last work,⁷ the feasibility of MCF was only proved with a simulation. No experiment was conducted. In this work, an experiment using a device based on the MCF theory is going to be introduced with the relationship between confinement ability and two variables, frequency of changing field and magnetic field strength.

Methods

An experiment was conducted to determine the correlations between magnetic field intensity, frequency, and confinement ability. As depicted in Figure 1, the device may be broken down into three basic components: a plasma generator, a MCF confinement system, and a single Langmuir probe.

Figure 1. Image of the design of the device.

Result and discussion

Readings of Langmuir is record and a graph of probe current and voltage is plotted, shown as Figure 2A and Figure 2B.¹⁰

Figure 2. (A) Probe current against probe voltage of plasma under a mixed confine fusion (MCF) confinement. (B) Probe current against probe voltage of plasma with no MCF confinement.

Second derivative of probe current against probe voltage is shown as Figure 3A and Figure 3B.¹⁰

Figure 3. (A) Second derivative of probe current against probe voltage under a mixed confine fusion (MCF) confinement. (B) Second derivative of probe current against probe voltage with no MCF confinement.

Prof. Azooz’s MATLAB program⁸ is used to analysis the data collected authors may be able to reproduce this analysis using open-source alternatives like Python or GNU Octave. With the usage of Prof. Azooz’s MATLAB program,⁸ with the output of ion density and electron temperature generated, the property of plasma in two situations is shown, it is found that plasma with no MCF confinement has ion density and electron temperature of 2.3081*10¹⁴ m^-3 and 39.3496 eV respectively. When plasma is under an MCF confinement, its ion density and electron temperature increased to 3.9803*10¹⁵ m^-3 and 105.1625 eV. This software is chosen because the input it requires, i.e. current and voltage readings across the Langmuir probe is identical to what is recorded in this experiment. After the data is inputted into the program, it would find out the best parameters from a₁ to a₄, that make the equation, equation 1.⁸ fit the data.

Then the result is generated within the usage of this fitted equation.

The ion saturation current is calculated with equation 2.⁸

Where H is the maxima number of I in the data inputted, V min is the minima number of V inputted.

Plasma potential can be calculated with equation 3.⁸

Vector VV in increments of 3 is created with equation 4.⁸

where V_max is the maxima number of voltage input.

Vector t in increments of 3 is created with equation 5.⁸

Electron temperature T can be calculated with equation 6.⁸

Where trapz(X,Y) integrates Y with respect to the coordinates or scalar spacing specified by X, E =t-Vp.

Ion density can be calculated with equation 7.⁸

Where Mi is the mass of ions in kg, in this work, it is assumed only Nitrogen ion is considered, so Mi is chosen as 2.32489449*10^-26 kg.

In order to find out the properties of plasma under a MCF confinement, Lawson’s criterion of product of ion density, ion temperature and energy confinement time is considered in this work.⁹ In order to find out the promotion, some assumptions are made. First, it is assumed the energy confinement time of plasma in all conditions are the same, as a consequence of usage of same plasma generator. Influence on energy confinement time caused by magnetic field confinement is ignored as it is too small and hard to measure. Second, it is also assumed that the plasma is under thermionic mode, i.e. ion has same temperature electrons, this assumption is made as a result of only electron temperature can be measured with Prof. Azooz’s program. After making these assumptions, the property of promotion of fusion efficiency can be written as equation 8.

Where ${\mathrm{n}}_{\mathrm{i}\mathrm{c}}$ and ${\mathrm{T}}_{\mathrm{e}\mathrm{c}}$ are ion density and electron temperature under MCF confinement, ${\mathrm{n}}_{\mathrm{i}\mathrm{nc}}$ and ${\mathrm{T}}_{\mathrm{e}\mathrm{nc}}$ are ion density and electron temperature with no MCF confinement.

In this work, it is found that p = 46.0880. Lawson’s criterion is used to evaluate fusion rate in fusion devices, p >1 means with the MCF magnetic field, a higher fusion rate existed, which provides evidence that MCF magnetic field provides a positive influence on fusion rate, i.e. evidence that the feasibility of using MCF as a fusion device. More dense and hotter plasma is found in the center of the chamber, as a consequence of that all particles in the plasma experienced a force towards the center of the chamber, due to MCF confinement. This is considered evidence of feasibility of confinement of MCF theory.

More evidence is found through the image shot with the camera, shown as Figure 4.

Figure 4. Image of plasma under a mixed confine fusion (MCF) confinement.

In Figure 4, it can be seen that a plasma sphere is confined by magnetic field. The sphere-shaped plasma fits the simulation of magnetic field in my previous work, i.e. the magnetic field energy is expected to be independent to direction,⁷ which produces a centripetal force on the particles, so that the plasma is expected to have a spheroidal shape.

Conclusions

In this work, an experiment it made to prove the feasibility of plasma confinement of MCF theory. It is found that the property of plasma under Lawson’s criterion is increased 46 times. This produces compelling evidence that MCF magnetic field can provide a confinement to plasma. Drawbacks of this study included the limited magnetic field and chamber size existed. It is suggested in further study, a larger chamber and a greater magnetic field should be used.